Moving text in VSE blurs or lags behind
Well thats interesting, you have discovered that animating the strip's "offset" value only produces a linear f-curve.



But you can change this curve so that the animation speeds up and slows down, instead of proceeding at a fixed rate. It will look more natural.
Change one of your windows to an F-Curve view, like this.
 See how the animation curve is a straight line.



Or you can press the T-Key to get this menu, choose Bezier (or any of the fun ones on the right, 'back' is my favourite).





Animating the Strip's Offset value will look far more natural now. Did you know that when you animate pretty much every other value in Blender, you will get the bezier curve automatically? Its just this one value doesn't do it like that.